Revisited apparent horizon entropy and GSL in modified gravity

TL;DR

This paper develops a universal formalism for apparent horizon entropy in modified gravity, incorporating an integral term, to assess the validity of the GSL across different models and redshifts, highlighting thermodynamics' deep link with gravity.

Contribution

It introduces a revised horizon entropy formula derived from modified Friedmann equations, applicable to various gravity models, and evaluates the GSL validity in these contexts.

Findings

Including the integral term can improve GSL validity at late times in some models.

The formalism is applicable to $f(T)$ and $f(R)$ gravity models.

The connection between thermodynamics and gravity is reinforced.

Abstract

This work presents a universal and revisited formalism for the entropy of the apparent horizon in modified gravity to investigate the validity of the Generalized Second Law (GSL) of thermodynamics. This revisited horizon entropy is constructed directly from the modified Friedmann equations in a non-flat Friedmann-Robertson-Walker (FRW) universe. The resulting entropy relation contains, beside the standard Bekenstein-Hawking term, an additional integral contribution that encodes the effective energy density and pressure generated by deviations from general relativity. Using this universal entropy formula, a compact expression for the GSL is derived. This formalism is then applied to some viable $f(T)$ and $f(R)$ gravity models, in order to re-evaluate the validity of the GSL as a function of redshift. The analysis demonstrates that including the integral term in the revisited entropy can relatively improve the late-time validity of the GSL for some of these models while living others unchanged, thereby reinforcing the profound connection between thermodynamics and gravity.